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Title: Comment on 'Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equation: Application to two-component Bose-Einstein condensates'

Abstract

In a recent paper, V. A. Brazhnyi and V. V. Konoto [Phys. Rev. E 72, 026616 (2005)] investigated the dynamics of vector dark solitons in two-component Bose-Einstein condensates. In the small amplitude limit, they deduced a coupled Korteweg-de Vries equation from the coupled Gross-Pitaevskii equations. They found that two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves exist. The slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into the stable fast solitons (corresponding to the upper branch of the dispersion law). However, our discussion shows that these results are incorrect.

Authors:
 [1]
  1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, 730070 (China)
Publication Date:
OSTI Identifier:
20778716
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.73.028601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; KORTEWEG-DE VRIES EQUATION; MATHEMATICAL EVOLUTION; NONLINEAR PROBLEMS; SCHROEDINGER EQUATION; SOLITONS; SOUND WAVES

Citation Formats

Xue Jukui. Comment on 'Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equation: Application to two-component Bose-Einstein condensates'. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.0.
Xue Jukui. Comment on 'Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equation: Application to two-component Bose-Einstein condensates'. United States. doi:10.1103/PHYSREVE.73.0.
Xue Jukui. Wed . "Comment on 'Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equation: Application to two-component Bose-Einstein condensates'". United States. doi:10.1103/PHYSREVE.73.0.
@article{osti_20778716,
title = {Comment on 'Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equation: Application to two-component Bose-Einstein condensates'},
author = {Xue Jukui},
abstractNote = {In a recent paper, V. A. Brazhnyi and V. V. Konoto [Phys. Rev. E 72, 026616 (2005)] investigated the dynamics of vector dark solitons in two-component Bose-Einstein condensates. In the small amplitude limit, they deduced a coupled Korteweg-de Vries equation from the coupled Gross-Pitaevskii equations. They found that two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves exist. The slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into the stable fast solitons (corresponding to the upper branch of the dispersion law). However, our discussion shows that these results are incorrect.},
doi = {10.1103/PHYSREVE.73.0},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 2,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • The dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of coupled one-dimensional nonlinear Schroedinger (NLS) equations. We consider the small-amplitude limit in which the coupled NLS equations are reduced to coupled Korteweg-de Vries (KdV) equations. For a specific choice of the parameters the obtained coupled KdV equations are exactly integrable. We find that there exist two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves. Slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into stablemore » fast solitons (corresponding to the upper branch of the dispersion law). Vector dark solitons of arbitrary depths are studied numerically. It is shown that effectively different parabolic traps, to which the two components are subjected, cause an instability of the solitons, leading to a splitting of their components and subsequent decay. A simple phenomenological theory, describing the oscillations of vector dark solitons in a magnetic trap, is proposed.« less
  • In their recent paper [Phys. Rev. A 71, 033622 (2005)], Seaman et al. studied Bloch states of the condensate wave function in a Kronig-Penney potential and calculated the band structure. They argued that the effective mass is always positive when a swallowtail energy loop is present in the band structure. In this Comment, we reexamine their argument by actually calculating the effective mass. It is found that there exists a region where the effective mass is negative even when a swallowtail is present. Based on this fact, we discuss the interpretation of swallowtails in terms of superfluidity.
  • In response to Danshita and Tsuchiya's comment on our work on nonlinear band theory, we show that the size of the region of the swallowtail with a negative effective mass is inversely proportional to the interaction strength, i.e., for large interaction strengths, the region becomes negligibly small. We explain why the appearance of swallowtails is not related to superfluidity, but instead to a more universal nonlinear feature valid for both signs of the underlying atomic interactions: period doubling.
  • We investigate the dynamics of two miscible superfluids experiencing fast counterflow in a narrow channel. The superfluids are formed by two distinguishable components of a trapped dilute-gas Bose-Einstein condensate (BEC). The onset of counterflow-induced modulational instability throughout the cloud is observed and shown to lead to the proliferation of dark-dark vector solitons. These solitons do not exist in single-component systems, exhibit intriguing beating dynamics, and can experience a transverse instability leading to vortex line structures. Experimental results and multidimensional numerical simulations are presented.
  • It is proven that periodically varying and sign definite nonlinearity in a general case does not prevent collapse in two-dimensional and three-dimensional nonlinear Schroedinger equations: at any oscillation frequency of the nonlinearity blowing up solutions exist. Contrary to the results known for a sign-alternating nonlinearity, an increase of the frequency of oscillations accelerates collapse. The effect is discussed from the viewpoint of scaling arguments. For the three-dimensional case a sufficient condition for the existence of collapse is rigorously established. The results are discussed in the context of the mean field theory of Bose-Einstein condensates with time-dependent scattering length.